In the images released on the official palace Facebook page, the adorable pair are dressed in pink and blue, to help well-wishers tell them apart.
Princess Charlene and Prince Albert look utterly besotted with the babies
Charlene's twins are the first royal heirs born in the tiny principality since the birth of their father 56 years ago. So Monaco celebrated in style, with church bells ringing for 15 minutes and 21 cannon shots fired for each child.
Gabriella arrived first on 10 December at 5.04pm, with her brother following two minutes later at 5.06pm. The little boy will be the next sovereign because of inheritance laws favouring males in the Mediterranean state.
Despite the pomp and protocol surrounding them, the 36-year-old royal is just like any new mum – utterly besotted with both her precious babies. In a long interview she spoke of the couple's joy, saying: "Every second with them is magical", adding that she's crazy in love with them.
Gabriella and Jacques' birth comes three years after Albert and Charlene's wedding
The father of the former Olympic swimmer also reiterated the excitement within the family. Just after the birth Michael Wittstock said the prince called him personally with the news.
"He called us and told us himself that things are good," said the delighted grandfather. "He gave us all the details, the babies’ names and all that, and said Charlene was doing very well."
Straight talking Mike, who has previously insisted that his new royal grandchildren would be treated the same as his others, added that he was keen to meet the little ones.
"We will now wait for things to settle down and then I will send my wife [Lynette] over first," he said. "That kind of thing is more of a woman’s job. Then I’ll go and join them a bit later."